Improved Interval-Valued Intuitionistic Fuzzy Entropy and Its Applications in Multi-attribute Decision Making Problems

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 367)


According to the defect of not fully reflecting the uncertainty, the improved definition and formula, which consider both aspects of uncertainty (fuzziness and lack of knowledge), of entropy for interval-valued intuitionistic fuzzy sets are proposed. The proposed entropy is used to solve multi-attribute decision making problems. Two numerical example verifies the appropriateness and effectiveness of the improved entropy for solving multi-attribute decision making problems.


Interval-valued intuitionistic fuzzy sets Interval-valued intuitionistic fuzzy entropy Uncertainty Hamming distance Multi-attribute decision making 


  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–356 (1965)CrossRefMathSciNetMATHGoogle Scholar
  2. 2.
    Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Atanassov, K., Gargov, G.: Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31(3), 343–349 (1989)CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    Burillo, P., Bustince, H.: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst. 78(3), 305–316 (1996)CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    Guo, X.: The discussion an expansion on measurement of fuzzy uncertainty. Xi an: Northwest University, pp. 43–45 (2004)Google Scholar
  6. 6.
    Liu, X., Zheng, S., Xiong, F.: Entropy and Subsethood for General Interval-valued Intuitionistic Fuzzy sets//LNAI 3613:FSKD. Springer, Berlin (2005)Google Scholar
  7. 7.
    Wang, P., Wei, C.: Constructing method of interval-valued intuitionistic fuzzy entropy. Comput. Eng. Appl. 47(2), 43–45 (2011)Google Scholar
  8. 8.
    Gao, Z., Wei, C.: Formula of interval-valued intuitionistic fuzzy entropy and its application. Comput. Eng. Appl. 48(2), 53–55 (2012)Google Scholar
  9. 9.
    Szmidt, E., Kacpryzk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst. 118(3), 467–477 (2001)CrossRefMATHGoogle Scholar
  10. 10.
    Zhang, Q., Jiang, S., Jia, B., et al.: Some information measures for interval-valued intuitionistic fuzzy sets. Inf. Sci. 180(24), 5130–5145 (2010)CrossRefMathSciNetMATHGoogle Scholar
  11. 11.
    Ye, J.: Multiattribute fuzzy decision-making method using entropy weights-based correlation coefficients for interval-valued intuitionistic fuzzy sets. Appl. Math. Model. 34(12), 3864–3870 (2010)CrossRefMathSciNetMATHGoogle Scholar
  12. 12.
    Ye, J.: Two effective measures of intuitionistic fuzzy entropy. Computing 87(1/2), 55–62 (2010)CrossRefMathSciNetMATHGoogle Scholar
  13. 13.
    Pal, N.R., Bustince, H., Pagola, M., et al.: Uncertainties with Atanassov’s intuitionistic fuzzy sets: fuzziness and lack of knowledge. Inf. Sci. 228, 61–74 (2013)CrossRefMathSciNetMATHGoogle Scholar
  14. 14.
    Szmidt, E., Kacpryzk, J., Bujnowski, P.: How to measure the amount of knowledge conveyed by Atanassov’s intuitionistic fuzzy sets. Inf. Sci. 257, 276–285 (2014)CrossRefGoogle Scholar
  15. 15.
    Lv, Y., Guo, S.: Entropy of intuitionistic fuzzy sets and its general forms. Comput. Eng. Appl. 47(28), 52–55 (2011)Google Scholar
  16. 16.
    Wang, C., Yao, D., Mao, J., et al.: Intuitionistic fuzzy multiple attributes decision making method based on entropy and correlation coefficient. J. Comput. Appl. 32(11), 3002–3004, 3017 (2012)Google Scholar
  17. 17.
    Shen, X., Guo, S.: New entropy formula for intuitionistic fuzzy sets and its applications. Comput. Eng. Appl. 49(24), 28–31 (2013)Google Scholar
  18. 18.
    Wu, T., Bai, L., Liu, R., et al.: New entropy formula of intuitionistic fuzzy sets and its application. Comput. Eng. Appl. 49(23), 48–51 (2013)Google Scholar
  19. 19.
    Gao, M., Sun, T., Zhu, J.: Reised axiomatic definition and structured formula of intuitionistic fuzzy entropy. Control Decis. 29(3), 470–474 (2014)MathSciNetMATHGoogle Scholar
  20. 20.
    Li, D.: Intuitionistic Fuzzy Set Decision and Game Analysis Methodologies, pp. 116–123. National Defence Industry Press, Beijing (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of SciencesSouthwest Petroleum UniversityChengduPeople’s Republic of China

Personalised recommendations